Auto Back Culling on export
The backface culling settings in the viewport don't affect how the model is exported, their effect is limited to how the model is displayed in the viewport in Blender. The normal of a face can be used to decide if a face is drawn or not, faces pointing away from view can be skipped. I suspect that's what's happening in those programs which are displaying the model in an unexpected way.

Most likely you want to recalculate the normals of your model and make then all outward facing (in editmode, select all faces, then Ctrl+N), then save, then export. 

If they are all pointing inwards, press Ctrl+F to get the Faces menu, and select Flip normals, then save, then export.

The mesh display panel has an option to show you the normals (here  displayed as light blue lines, the size of which is defined in the Size slider):